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436
Achieving MinimumCost Multicast: A Decentralized Approach Based on Network Coding
 IN PROCEEDINGS OF IEEE INFOCOM
, 2005
"... We present decentralized algorithms that compute minimumcost subgraphs for establishing multicast connections in networks that use coding. These algorithms, coupled with existing decentralized schemes for constructing network codes, constitute a fully decentralized approach for achieving minimumco ..."
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Cited by 116 (15 self)
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We present decentralized algorithms that compute minimumcost subgraphs for establishing multicast connections in networks that use coding. These algorithms, coupled with existing decentralized schemes for constructing network codes, constitute a fully decentralized approach for achieving minimumcost multicast. Our approach is in sharp contrast to the prevailing approach based on approximation algorithms for the directed Steiner tree problem, which is suboptimal and generally assumes centralized computation with full network knowledge. We also give extensions beyond the basic problem of fixedrate multicast in networks with directed pointtopoint links, and consider the problem of minimumenergy multicast in wireless networks as well as the case of a concave utility function at the sender.
Stability of endtoend algorithms for joint routing and rate control
"... Dynamic multipath routing has the potential to improve the reliability and performance of a communication network, but carries a risk. Routing needs to respond quickly to achieve the potential benefits, but not so quickly that the network is destabilized. This paper studies how rapidly routing can ..."
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Cited by 110 (1 self)
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Dynamic multipath routing has the potential to improve the reliability and performance of a communication network, but carries a risk. Routing needs to respond quickly to achieve the potential benefits, but not so quickly that the network is destabilized. This paper studies how rapidly routing can respond, without compromising stability. We present a sufficient condition for the local stability of endtoend algorithms for joint routing and rate control. The network model considered allows an arbitrary interconnection of sources and resources, and heterogeneous propagation delays. The sufficient condition we present is decentralized: the responsiveness of each route is restricted by the roundtrip time of that route alone, and not by the roundtrip times of other routes. Our results suggest that stable, scalable loadsharing across paths, based on endtoend measurements, can be achieved on the same rapid timescale as rate control, namely the timescale of roundtrip times.
Multipath TCP: A joint congestion control and routing scheme to exploit path diversity on the internet
 IEEE/ACM Transactions on Networking
, 2006
"... We consider the problem of congestionaware multipath routing in the Internet. Currently, Internet routing protocols select only a single path between a source and a destination. However, due to many policy routing decisions, singlepath routing may limit the achievable throughput. In this paper, w ..."
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Cited by 101 (3 self)
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We consider the problem of congestionaware multipath routing in the Internet. Currently, Internet routing protocols select only a single path between a source and a destination. However, due to many policy routing decisions, singlepath routing may limit the achievable throughput. In this paper, we envision a scenario where multipath routing is enabled in the Internet to take advantage of path diversity. Using minimal congestion feedback signals from the routers, we present a class of algorithms that can be implemented at the sources to stably and optimally split the flow between each sourcedestination pair. We then show that the connectionlevel throughput region of such multipath routing/congestion control algorithms can be larger than that of a singlepath congestion control scheme. 1
Approximate Primal Solutions and Rate Analysis for Dual Subgradient Methods
, 2007
"... We study primal solutions obtained as a byproduct of subgradient methods when solving the Lagrangian dual of a primal convex constrained optimization problem (possibly nonsmooth). The existing literature on the use of subgradient methods for generating primal optimal solutions is limited to the met ..."
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Cited by 82 (7 self)
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We study primal solutions obtained as a byproduct of subgradient methods when solving the Lagrangian dual of a primal convex constrained optimization problem (possibly nonsmooth). The existing literature on the use of subgradient methods for generating primal optimal solutions is limited to the methods producing such solutions only asymptotically (i.e., in the limit as the number of subgradient iterations increases to infinity). Furthermore, no convergence rate results are known for these algorithms. In this paper, we propose and analyze dual subgradient methods using averaging to generate approximate primal optimal solutions. These algorithms use a constant stepsize as opposed to a diminishing stepsize which is dominantly used in the existing primal recovery schemes. We provide estimates on the convergence rate of the primal sequences. In particular, we provide bounds on the amount of feasibility violation of the generated approximate primal solutions. We also provide upper and lower bounds on the primal function values at the approximate solutions. The feasibility violation and primal value estimates are given per iteration, thus providing practical stopping criteria. Our analysis relies on the Slater condition and the inherited boundedness properties of the dual problem under this condition.
Crosslayer optimization in TCP/IP networks
 IEEE/ACM Transactions on Networking
, 2005
"... Abstract — TCP–AQM can be interpreted as distributed primaldual algorithms to maximize aggregate utility over source rates. We show that an equilibrium of TCP/IP, if exists, maximizes aggregate utility over both source rates and routes, provided congestion prices are used as link costs. An equilibr ..."
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Cited by 72 (12 self)
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Abstract — TCP–AQM can be interpreted as distributed primaldual algorithms to maximize aggregate utility over source rates. We show that an equilibrium of TCP/IP, if exists, maximizes aggregate utility over both source rates and routes, provided congestion prices are used as link costs. An equilibrium exists if and only if this utility maximization problem and its Lagrangian dual have no duality gap. In this case, TCP/IP incurs no penalty in not splitting traffic across multiple paths. Such an equilibrium, however, can be unstable. It can be stabilized by adding a static component to link cost, but at the expense of a reduced utility in equilibrium. If link capacities are optimally provisioned, however, pure static routing, which is necessarily stable, is sufficient to maximize utility. Moreover singlepath routing again achieves the same utility as multipath routing at optimality. Index Terms — Utility optimization, congestion control, TCP
Scheduling efficiency of distributed greedy scheduling algorithms in wireless networks
 in INFOCOM
, 2006
"... Abstract — We consider the problem of distributed scheduling in wireless networks subject to simple collision constraints. We define the efficiency of a distributed scheduling algorithm to be the largest number (fraction) such that the throughput under the distributed scheduling policy is at least e ..."
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Cited by 70 (1 self)
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Abstract — We consider the problem of distributed scheduling in wireless networks subject to simple collision constraints. We define the efficiency of a distributed scheduling algorithm to be the largest number (fraction) such that the throughput under the distributed scheduling policy is at least equal to the efficiency multiplied by the maximum throughput achievable under a centralized policy. For a general interference model, we prove a lower bound on the efficiency of a distributed scheduling algorithm by first assuming that all the traffic only uses onehop of the network. We also prove that the lower bound is tight in the sense that for any fraction larger than the lower bound, we can find a topology and an arrival rate vector within the fraction of the capacity region, such that the network is unstable under a greedy scheduling policy. We then extend our results to a more general multihop traffic scenario and show that similar scheduling efficiency results can be established by introducing prioritization or regulators to the basic greedy scheduling algorithm. Index Terms — Multihop wireless networks, scheduling, greedy algorithms, resource allocation
Layering as optimization decomposition
 PROCEEDINGS OF THE IEEE
, 2007
"... Network protocols in layered architectures have historically been obtained on an ad hoc basis, and many of the recent crosslayer designs are conducted through piecemeal approaches. They may instead be holistically analyzed and systematically designed as distributed solutions to some global optimiza ..."
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Cited by 64 (23 self)
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Network protocols in layered architectures have historically been obtained on an ad hoc basis, and many of the recent crosslayer designs are conducted through piecemeal approaches. They may instead be holistically analyzed and systematically designed as distributed solutions to some global optimization problems. This paper presents a survey of the recent efforts towards a systematic understanding of “layering ” as “optimization decomposition”, where the overall communication network is modeled by a generalized Network Utility Maximization (NUM) problem, each layer corresponds to a decomposed subproblem, and the interfaces among layers are quantified as functions of the optimization variables coordinating the subproblems. There can be many alternative decompositions, each leading to a different layering architecture. This paper summarizes the current status of horizontal decomposition into distributed computation and vertical decomposition into functional modules such as congestion control, routing, scheduling, random access, power control, and channel coding. Key messages and methods arising from many recent work are listed, and open issues discussed. Through case studies, it is illustrated how “Layering as Optimization Decomposition” provides a common language to think
Joint asynchronous congestion control and distributed scheduling for multihop wireless networks
 in the Proceedings IEEE Infocom
"... Abstract — We consider a multihop wireless network shared by many users. For an interference model that only constrains a node to either transmit or receive at a time, but not both, we propose an architecture for fair resource allocation that consists of a distributed scheduling algorithm operating ..."
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Cited by 62 (17 self)
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Abstract — We consider a multihop wireless network shared by many users. For an interference model that only constrains a node to either transmit or receive at a time, but not both, we propose an architecture for fair resource allocation that consists of a distributed scheduling algorithm operating in conjunction with an asynchronous congestion control algorithm. We show that the proposed joint congestion control and scheduling algorithm supports at least onethird of the throughput supportable by any other algorithm, including centralized algorithms. I.
Global Stability of Internet Congestion Controllers with Heterogeneous Delays
, 2004
"... In this paper, we study the problem of designing globally stable, scalable congestion control algorithms for the Internet. Prior work has primarily used linear stability as the criterion for such a design. Global stability has been studied only for single node, single source problems. Here, we obtai ..."
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Cited by 58 (1 self)
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In this paper, we study the problem of designing globally stable, scalable congestion control algorithms for the Internet. Prior work has primarily used linear stability as the criterion for such a design. Global stability has been studied only for single node, single source problems. Here, we obtain conditions for a general topology network accessed by sources with heterogeneous delays. We obtain a sufficient condition for global stability in terms of the increase/decrease parameters of the congestion control algorithm and the price functions used at the links.